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CHAPTER 2
EXERCISES 2.1
1-6: Recall that the maturity value is the amount to be paid to the lender at the end of
the noteâ&#x20AC;&#x2122;s term to pay off the loan. The proceeds is that amount given to the
borrower/buyer for the note. The proceeds is the same things as what we would call the
principal if we were looking at things as simple interest.
The discount is the difference between the proceeds and the maturity value. The
discount is equal to what we would call the interest if we were looking at things as simple
interest.
1.

The amount of the discount is $1,000 - $982.56 = $17.44
D = MdT
$17.44 = $1,000(d)(91/365)
17.44 = 249.3150685 d
Divide both sides by 249.3150685
d = 0.0699516484 = 7.00%
27.
The term of this loan is 15 – 1 = 14 days. (You could also calculate the number
of days by finding the Julian dates for May 15 and May 1 and subtracting, but since the
dates fall in the same month this is not really necessary to find the term.)
D = MdT
D = $17,500,000(0.0398)(14/365)
D = $26,715.07
The proceeds are $17,500,000 - $26,715.07 = $17,473,284.93

2-4

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28.

a.
The amount of the discount is $5,000 - $4,905.75 = $94.25
D = MdT
$94.25 = ($5,000)(0.04)T
94.25 = 200T
Divide both sides by 200
T = 0.47125 years
Multiply by 365 and round to convert years to days
T = 172 days
b.
March 12 is day 59+12 = 71. 172 days after that is day 71+172 = 243. This date
is actually one of the numbers listed in the abbreviated table. The maturity date is August
31.
29.

The amount of the discount is $100,000 - $99,353.29 = $646.71
D = MdT
$646.71 = $100,000(0.0444)T
646.71 = 4440T
Divide both sides by 4440
T = 0.1456554054 years
Multiply by 365 and round to convert years to days
T = 53 days
April 3 is day 90+3 = 93. 53 days after that is day 93+53=146.
The largest number in the abbreviated table less than 146 is 120, the end of April. So the
maturity date is 146-120 = 26 days after that: May 26, 2007.
30.

The amount of the discount is $150,000 - $117,300 = $32,700
D = MdT
$32,700 = $150,000(d)(9/12)
32,700 = 112,500 d
Divide both sides by 112,500
d = 29.07%
Note that this rate is based on an assumed remaining life expectancy. Because the
insuredâ&#x20AC;&#x2122;s actual time left can not be known for certain, the actual simple discount rate
cannot be known in advance.

2-5

Timothy J. Biehler
EXERCISES 2.2
1-4.

Recall the definition of these terms.
Both the principal (a) and proceeds (e) refer to the amount borrowed.
The maturity value (b) and (f) refers to the amount to be paid by the borrower to
the lender at the end of the loanâ&#x20AC;&#x2122;s term, whether simple interest or simple discount.
The amount of interest (c) is the same as the amount of discount (g).
The face value (d) when using simple interest is the same as the principal. When
using simple discount, the face value (h) is the same as the maturity value.
1.

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23.

D = MdT
D = ($1,800,000)(0.095)(3/12)
D = $42,750
So the company would receive proceeds of $1,800,000 - $42,750 = $1,757,250
To compare the two offers, we need to know the equivalent simple interest rate, to
be able to compare it to the other offerâ&#x20AC;&#x2122;s simple interest rate.
I = PRT
$42,750 = ($1,757,250)(R)(3/12)
42,750 = 439,312.5 R
R = 9.73%
Even though 9.63% sounds like a higher rate compared to 9.5%, in actuality 9.63% is a
better deal since the 9.5% discount rate is equivalent to a 9.73% interest rate.
24.

$1,295 - $1,249.35 = $45.65

25.
The amount of discount/amount of interest is $45.65. We can now calculate the
simple discount rate.
I = PRT
$45.65 = $1249.35(R)(45/365)
45.65 = 154.0294521 R
R = 29.64%
This is actually higher than the rate charged by the credit card.
26.

I = PRT
I = ($14,357)(0.15)(100/365)
I = $590.01
The maturity value is $14,357 + $590.01 = $14,947.01
D = MdT
$590.01 = ($14,947.01)d(100/365)
590.01 = 4,095.071233 d
d = 14.41%
27.
The simple interest rate should always be higher than the simple discount rate,
because the principal is always less than the maturity value. 7/31/07 must be the
misprint.
28.

D = MdT
D = ($10,000)(0.06)(1/12)
D = $50
The proceeds are $10,000 - $50 = $9,950
I = PRT
$50 = ($9,950)(R)(1/12)
50 = 829.1666667 R
R = 6.03%
b)
Done the same way as a) but with T=3/12
c)
Done the same was as a) but with T = 6/12/07
d)
Done the same way as a) but with T = 1
e)
The point of these comparisons is that there is no one simple interest rate that is
equivalent to a given discount rate. The equivalent simple interest rate for a given
situation depends not only on the discount rate, but also on the term

I = PRT
I = ($3,000)(0.0845)(125/365)
I = $86.82
The maturity value is $3,000 + $86.82 = $3,086.82
b)
The note was sold 45 days after it started. Since the original term was 125 days,
this means that 125 – 45 = 80 days were left.
D = MdT
D = ($3,086.82)(0.0768)(80/365)
D = $51.96
The proceeds are $3,086.82 - $51.96 = $3,034.86
2.

a)
I = PRT
I = $5,255(0.1225)(200/365)
I = $352.73
The maturity value is $5,225 + $352.73 = $5,607.73
b)
The note was sold 80 days after it started. Since the original term was 200 days,
this means that 200 – 80 = 120 days were left.
D = MdT
D = $5,607.73(0.0928)(120/365)
D = $171.09
The proceeds are $5,607.73 - $171.09 = $5,436.64
3.

I = PRT
I = ($2,750)(0.16)(100/365)
I = $120.55
The maturity value is $2,750 + $120.55 = $2,870.55
The problem states that the note was sold when 30 days were left until maturity.
D = MdT
D = ($2,870.55)(0.12)(30/365)
D = $28.31
The proceeds are $2,870.55 - $28.31 = $2,842.24
4.

I = PRT
I = $8,000(0.103)(220/365)
I = $496.66
The maturity value is $8,000 + $496.66 = $8,496.66
The note was sold 90 days after it started. Since the original term was 220 days, this
means that 220 – 90 = 130 days were left.
D = MdT
D = ($8,496.66)(0.114)(130/365)
D = $344.99
The proceeds are $8,496.66 - $344.99 = $8,151.67

2-13

Timothy J. Biehler

5.
January 16 is day 16; March 25 is day 59+25 = 84; November 15 is day 304 +
15 = 319. (We are assuming this is not a leap year.)
The note’s original term was 319 – 16 = 303 days.
I = PRT
I = ($10,000)(0.0992)(303/365)
I = $823.50
The maturity value is $10,000 + $823.50 = $10,823.50
When the note was sold, the remaining term was 319 – 84 = 235 days.
D = MdT
D = $10,823.50(0.0825)(235/365)
D = $574.91
The proceeds are $10,823.50 - $574.91 = $10,248.59
6.
February 11 is day 31+11 = 42; February 26 is day 31+26 = 57; July 5 is day
181+5 = 186.
The note’s original term was 186 – 42 = 144 days.
I = PRT
I = ($2,500)(0.1502)(144/365)
I = $148.14
The maturity value was $2,500 + $148.14 = $2,648.14
When the note was sold, the remaining term was 186 – 57 = 129 days.
D = MdT
D = ($2,648.14)(0.0931)(129/365)
D = $87.13
The proceeds are $2,648.14 - $87.13 = $2,561.01
7.

October 18 is day 273 + 18 = 291; November 23 is day 304+23 = 327.
I = PRT
I = ($6,000)(0.0675)(200/365)
I = $221.92
The maturity value is $6,000 + $221.92 = $6,221.92.
The time between when Neela made the loan and when she sold the note was 327
– 291 = 36 days. That means there were 200 – 36 = 164 days left when it was sold.
D = MdT
D = ($6,221.92)(0.1281)(164/365)
D = $358.12
The proceeds are $6,221.92 - $358.12 = $5,863.80.

2-14

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8.
289.

April 30 is day 120; February 7 is day 31+7 = 38; October 16 is day 273+16 =

The note extends across part of 2006 and part of 2007. The note’s life in 2006 is
365 – 120 = 245 days. The note’s life in 2007 is 38 days. In total, the note’s term is 283
days.
I = PRT
I = ($538,000)(0.0459)(283/365)
I = $19,146.46
The maturity value is $538,000 + $19,146.46 = $557,146.46
When the note was sold, it still had 365 – 289 = 76 days to run in 2006 and 38
days in 2007, for a total remaining term of 114 days.
D = MdT
D = ($557,146.46)(0.06)(114/365)
D = $10,440.77
The proceeds are $557,146.46 - $10,440.77 = $546,705.69
9.

This is a discount note to begin with. When Ronda bought it it had 188 – 126 =
62 days left.
D = MdT
D = ($10,000)(0.0653)(62/365)
D = $110.92
So Ronda bought the note for $10,000 - $110.92 = $9,889.08.
Ronda’s point of view. She held the note for 170 – 126 = 44 days. From her point of
view:
$9,889.08
$9,984.50
|---------------------------------------------------|
44 days
I = PRT
$95.42 = ($9,889.08)(R)(44/365)
95.42 = 1,192.108274 R
R = 8.00%
27.

Chico is not affected by the sale. 13.29%

28.

April 1 is day 90+1 = 91; May 12 is day 120+12 = 132.
I = PRT
I = ($40,000)(0.1163)(100/365)
I = $1,274.52
The maturity value is $40,000 + $1,274.52 = $41,274.52
The original lender held the note for 132 – 91 = 41 days. So when it was sold it had 100
– 41 = 59 days left.
D = MdT
D = ($41,274.52)(0.2439)(59/365)
D = $1,627.25
The proceeds were $41,274.52 - $1,627.25 = $39,647.27

32.
Even though both the simple interest rate and the simple discount rate are 5%, the
simple discount rate is applied to the maturity value, so it means that when the note was
sold, the amount of discount taken would be more than the amount of interest earned at
5%. Therefore, the interest rate earned must be less than 5%.
If you still have doubts about this, try it for yourself, making up the details of the
amount borrowed and the times involved.

Calculate the maturity value: $26,061.64
D = MdT
$260.64 = $26,061.64(0.08)T
T = 46 days were left when the note was sold.
So the note was sold 109 days after July 5.
July 5 is day 181+5 = 186, so the note was sold on day 186+109 = 295.
Converting from Julian to regular date we get October 22.

I = PRT
I = ($8,912.35)(0.085)(125/365)
I = $259.43
The maturity value is $8,912.35 + $259.43 = $9,171.78
17.
April 17 is day 90+17 = 107. The note matures 100 days later on day 107+100 =
207. The end of June is day 181, so the note matures 207 – 181 = 26 days later, on July
26.
I = PRT
31.58 = P(0.0785)(100/365)
31.58 = (0.0215068493)P
P = $1468.37
The maturity value is $1468.37 + $31.58 = $1,499.95.
18.

$5000 - $4848.59 = $151.41

19.

The borrower is unaffected by the sale of the note. 7%.

20.
a)
April 1 is day 90+1 = 91. The note can run for 365 – 91 = 274 days in
1999, leaving 300 – 274 = 26 days to run into 2000. That takes the maturity date to
January 26, 2000. The fact that 2000 is a leap year is irrelevant since we did not cross
the leap day.
b)
I = PRT
I = ($20,000)(0.1275)(300/365)
I = $2095.89
The maturity value is $20,000 + $2,095.89 = $22,059.89.
21.

$3,000 - $2,857.16 = $142.84

22.

Recall that bankers rule means that we assume 360 days per year.
D = MdT
D = ($3,000)(0.06)(45/360)
D = $37.50
The proceeds are $5000 - $37.50 = $4,962.50
23.
April 1 is day 90+1 = 91. July 8 is day 181+8 = 189.
I = PRT
I = ($15,000)(0.0875)(200/365)
I = $719.18
The maturity value of the note is $15,000 + $719.18 = $15,719.18
The lender held the note for 189 – 91 = 98 days. That leaves 200 – 98 = 102 days to go
when it was sold.